What is the surface area of a cylinder with base radius 2 and height 9? Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal.

To calculate the surface area of a cylinder, we need to find the area of the two circular bases and the area of the curved surface (the lateral area).Step 1: Calculate the area of the two circular bases.The area of one circle is given by the formula \(A = \pi r^2\), where \(r\) is the radius of the circle. Since the cylinder has two bases, we will multiply the area of one base by 2.Given that the radius \(r = 2\), the area of one base is:\[A_{base} = \pi \times 2^2 = 4\pi\]Since there are two bases, the total area for both bases is:\[A_{total bases} = 2 \times A_{base} = 2 \times 4\pi = 8\pi\]Step 2: Calculate the lateral surface area of the cylinder.The lateral surface area is the area of the rectangle that wraps around the cylinder, which can be found by multiplying the circumference of the base by the height of the cylinder.The circumference of the base is given by \(C = 2\pi r\). With \(r = 2\), the circumference is:\[C = 2\pi \times 2 = 4\pi\]The height \(h = 9\), so the lateral surface area is:\[A_{lateral} = C \times h = 4\pi \times 9 = 36\pi\]Step 3: Add the areas of the bases and the lateral surface to find the total surface area.\[A_{total} = A_{total bases} + A_{lateral} = 8\pi + 36\pi = 44\pi\]Answer:The surface area of the cylinder is \(44\pi\) square units. If we use \(\pi \approx 3.14\), then the surface area in decimal form is:\[A_{total} = 44 \times 3.14 = 138.16\]So, the surface area of the cylinder is approximately 138.16 square units when using \(\pi \approx 3.14\).